On inhibition of the Rayleigh–Taylor instability by a horizontal magnetic field in ideal MHD fluids with velocity damping

Jiang, Fei; Jiang, Song; Zhao, Youyi

doi:10.1016/j.jde.2022.01.013

Cited by 16 publications

(4 citation statements)

References 38 publications

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“…(3) Our stability result can be viewed as a continuation of the previous work of the inviscid case with velocity damping in [31]. However, we develop a new idea to capture the high-order normal (spacial) derivatives of the deviation function of fluid particles from the viscosity term under the Navier boundary condition, and the details will be further discussed after introducing our stability result in Theorem 1.1.…”

Section: Introductionmentioning

confidence: 91%

“…Lemma A.6. Diffeomorphism mapping theorem (see [31,Lemma A.8]): There exists a sufficiently small constant γ ∈ (0, 1), depending on Ω, such that for any ς ∈ H 3 s satisfying ∇ς 2 γ, ψ := ς + y (after possibly being redefined on a set of measure zero with respect to variable y) satisfies the same diffeomorphism properties as ζ in (1.15) and (1.16), and inf y∈Ω det(∇ς + I) 1/4. Lemma A.7.…”

Section: Appendix a Analysis Toolsmentioning

confidence: 99%

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On Inhibition of Rayleigh--Taylor Instability by a Horizontal Magnetic Field in Non-resistive MHD Fluids: the Viscous Case

Jiang¹,

Jiang²,

Zhao³

2022

Preprint

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It is still open whether the phenomenon of inhibition of Rayleigh-Taylor (RT) instability by a horizontal magnetic field can be mathematically verified for a non-resistive viscous magnetohydrodynamic (MHD) fluid in a two-dimensional (2D) horizontal slab domain, since it was roughly proved in the linearized case by Wang in [41]. In this paper, we prove such inhibition phenomenon by the (nonlinear) inhomogeneous, incompressible, viscous case with Navier (slip) boundary condition. More precisely, we show that there is a critical number of field strength m C , such that if the strength |m| of a horizontal magnetic field is bigger than m C , then the small perturbation solution around the magnetic RT equilibrium state is algebraically stable in time. In addition, we also provide a nonlinear instability result for the case |m| ∈ [0, m C ). The instability result presents that a horizontal magnetic field can not inhibit the RT instability, if it's strength is too small.

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Section: Introductionmentioning

confidence: 91%

Section: Appendix a Analysis Toolsmentioning

confidence: 99%

On Inhibition of Rayleigh--Taylor Instability by a Horizontal Magnetic Field in Non-resistive MHD Fluids: the Viscous Case

Jiang¹,

Jiang²,

Zhao³

2022

Preprint

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“…Chen et al studied the linear RTI of stratified fluids and the effects of elasticity and magnetic fields on it [52]. Jiang et al reported the phenomenon of inhibition of RTI in the inviscid, inhomogeneous and incompressible fluid by applying horizontal magnetic field along velocity damping [53].…”

Section: Review Of the Current Statusmentioning

confidence: 99%

Plasma Waves and Rayleigh–Taylor Instability: Theory and Application

Singh¹,

Vidhani²,

Yogi³

et al. 2023

Plasma Science - Recent Advances, New Perspectives and Applications

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The presence of plasma density gradient is one of the main sources of Rayleigh–Taylor instability (RTI). The Rayleigh–Taylor instability has application in meteorology to explain cloud formations and in astrophysics to explain finger formation. It has wide applications in the inertial confinement fusion to determine the yield of the reaction. The aim of the chapter is to discuss the current status of the research related to RTI. The current research related to RTI has been reviewed, and general dispersion relation has been derived under the thermal motion of electron. The perturbed densities of ions and electrons are determined using two fluid approach under the small amplitude of oscillations. The dispersion equation is derived with the help of Poisson’s equation and solved numerically to investigate the effect of various parameters on the growth rate and real frequency. It has been shown that the real frequency increases with plasma density gradient, electron temperature and the wavenumber, but magnetic field has opposite effect on it. On the other hand, the growth rate of instability increases with magnetic field and density gradient, but it decreases with electron temperature and wave number.

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“…, then for any f satisfying f ∈ L p (I T , H i ) and f t ∈ L p (I T , H i−1 ), where 1 i 3, then [20,Lemma A.10] for the proof.…”

Section: Appendix a Analytic Toolsmentioning

confidence: 99%

Global Solutions of Three-dimensional Inviscid MHD Fluids with Velocity Damping in Horizontally Periodic Domains

Jiang¹,

Jiang²,

Zhao³

2021

Preprint

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The two-dimensional (2D) existence result of global(-in-time) solutions for the motion equations of incompressible, inviscid, non-resistive magnetohydrodynamic (MHD) fluids with velocity damping had been established in [Wu-Wu-Xu, SIAM J. Math. Anal. 47 (2013), 2630-2656. This paper further studies the existence of global solutions for the three-dimensional (a dimension of real world) initial-boundary value problem in a horizontally periodic domain with finite height. Motivated by the multi-layers energy method introduced in [Guo-Tice, Arch. Ration. Mech. Anal. 207 (2013), 459-531], we develop a new type of two-layer energy structure to overcome the difficulty arising from three-dimensional nonlinear terms in the MHD equations, and thus prove the initial-boundary value problem admits a unique global solution. Moreover the solution has the exponential decay-in-time around some rest state. Our two-layer energy structure enjoys two features: (1) the lower-order energy (functional) can not be controlled by the higher-order energy. (2) under the a priori smallness assumption of lower-order energy, we first close the higher-order energy estimates, and then further close the lower-energy estimates in turn.

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On inhibition of the Rayleigh–Taylor instability by a horizontal magnetic field in ideal MHD fluids with velocity damping

Cited by 16 publications

References 38 publications

On Inhibition of Rayleigh--Taylor Instability by a Horizontal Magnetic Field in Non-resistive MHD Fluids: the Viscous Case

On Inhibition of Rayleigh--Taylor Instability by a Horizontal Magnetic Field in Non-resistive MHD Fluids: the Viscous Case

Plasma Waves and Rayleigh–Taylor Instability: Theory and Application

Global Solutions of Three-dimensional Inviscid MHD Fluids with Velocity Damping in Horizontally Periodic Domains

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